Open Free Books maps chapters to popular school and exam frameworks worldwide. This page summarises how those curricula differ in philosophy and pacing, and how our catalog chapters align. Curriculum labels appear only here and in catalog filters — not inside lesson pages.
Legend
- core — explicit unit in that framework at this level
- ext — extension, elective, or higher tier only
- rel — related supporting topic, not a named syllabus unit
- — — not mapped for this chapter
Framework comparison
| Dimension | Foundation (OFB) | DSE / HKDSE | IGCSE | A-Level | AP (US) | IB AA | IB AI | Common Core | Singapore | UK GCSE | Gaokao |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Philosophy | Prerequisite-first bridge from arithmetic to secondary topics; CPA-friendly sequencing. | Exam-focused compulsory syllabus (S4–S6); applied contexts in Number & Algebra. | Cambridge international; broad Number, Algebra, Geometry, Statistics. | Two-year depth in Pure, Statistics, Mechanics; proof and abstraction. | Elective acceleration; AP Calculus AB/BC in Grade 12 for many students. | Pure, theoretical; proofs, calculus, abstract reasoning for STEM. | Applied modelling; statistics, technology, real-world interpretation. | Conceptual understanding + mathematical practices across K–12. | Mastery; “teach less, learn more”; CPA and bar models. | Key Stages; mandatory GCSE at 16; tiered papers. | National entrance exam; extreme rigour and time pressure. |
| Pacing | Split integers vs rationals/proportion before synthesis chapter. | Compulsory part bundles secondary algebra after junior foundation. | Linear progression to IGCSE at ~16. | Slower two-year HL/AL build than single-year AP calculus. | Algebra I → Geometry → Algebra II; calculus optional via AP. | SL/HL tracks; AA emphasises theory. | SL/HL tracks; AI emphasises data and modelling. | More topics per year than Singapore; grade-level benchmarks. | Deep focus on fewer topics per level. | KS3 then GCSE; optional A-Level. | Integrated secondary syllabus toward one high-stakes exam. |
| Distinctive focus | Explicit graph prerequisites; global labels in catalog only. | Three strands: Number & Algebra, Measures/Shape/Space, Data Handling. | International portability; strong algebra and trig base. | Complex numbers, induction, mechanics optional components. | Standardised AP exams; college credit pathway. | Formal proofs and advanced calculus preparation. | Calculator-forward statistics and function modelling. | Reasoning, modelling, precision in standards. | Number bonds, mental strategies, visualisation. | Tiered foundation/higher GCSE content. | Multi-step synthesis under exam conditions. |
Framework notes
Foundation (Open Free Books)
Our Foundation track is not a national syllabus — it is the pre-secondary path in this catalog. Research on middle-years progression (integers, rational numbers, proportion) showed a gap between whole-number written calculation and secondary “directed numbers & rates” work. Five planned chapters now sit in the prerequisite graph before the live synthesis chapter.
Hong Kong DSE (compulsory)
The HKDSE compulsory mathematics curriculum organises secondary topics into Number & Algebra, Measures, Shape and Space, and Data Handling. Our chapter graph and strand layout follow that shape while remaining usable for learners outside Hong Kong.
Singapore Mathematics
Emphasises mastery through the Concrete–Pictorial–Abstract sequence, number bonds, and bar modelling. Fewer topics per year, deeper fluency — a useful contrast to broader spiral systems.
Common Core (United States)
Shifts K–12 toward conceptual understanding and mathematical practices (reasoning, modelling, precision). High school often follows Algebra I, Geometry, Algebra II; calculus is commonly via AP rather than mandated in the core standards.
IGCSE, GCSE, A-Level (UK / Cambridge)
GCSE and IGCSE provide broad 14–16 coverage; A-Level allows two years for pure mathematics, statistics, and mechanics — generally more time for abstraction than a single-year AP calculus course.
International Baccalaureate
Students choose Analysis & Approaches (theory, proofs, calculus) or Applications &
Interpretation (statistics, modelling, technology). The catalog uses one IB filter chip;
this page separates AA and AI for comparison.
Gaokao (China)
The national college entrance mathematics paper integrates advanced algebra, calculus, probability, and coordinate geometry under high-stakes time limits — typically more synthesis per item than many Western school-leaving exams.
Chapter coverage
Catalog filter chips still match any framework with a non-empty mapping. List and map badges show framework labels only.
| Chapter | Foundation | DSE | IGCSE | A-Level | AP | IB | Common Core | Singapore | UK GCSE | Gaokao |
|---|---|---|---|---|---|---|---|---|---|---|
| Zero and one | core | rel | core | rel | rel | rel | core | core | core | rel |
| Counting and numbers | core | rel | core | rel | rel | rel | core | core | core | rel |
| Basic math notation | core | rel | core | rel | rel | rel | core | core | core | rel |
| Properties of operations | core | rel | core | rel | rel | rel | core | core | core | rel |
| Written calculation | core | rel | core | rel | rel | rel | core | core | core | rel |
| Integer foundations | core | rel | core | rel | rel | rel | core | core | core | rel |
| Fractions and decimals | core | rel | core | rel | rel | rel | core | core | core | rel |
| Percentage applications | core | rel | core | rel | rel | rel | core | core | core | rel |
| Ratios & rates foundations | core | rel | core | rel | rel | rel | core | core | core | rel |
| Polynomials: expansion & factorisation | rel | core | core | core | rel | core | core | core | core | core |
| Algebraic fractions & formulas | rel | core | core | core | rel | core | rel | rel | core | rel |
| Linear equations in two unknowns | rel | core | core | core | rel | core | core | core | core | core |
| Linear inequalities in one unknown | — | core | core | rel | rel | rel | core | rel | core | rel |
| Laws of indices | rel | core | core | core | core | core | core | core | core | core |
| Quadratic equations | rel | core | core | core | core | core | core | core | core | core |
| Factor & remainder theorems | — | ext | rel | ext | rel | ext | — | — | — | rel |
| Complex numbers | — | ext | rel | ext | rel | ext | — | — | — | rel |
| Functions & graphs | rel | core | core | core | core | core | core | core | core | core |
| Exponential & logarithmic functions | rel | ext | core | core | core | core | core | rel | core | core |
| Sequences & series | rel | core | core | core | rel | core | rel | rel | core | core |
| Variations | — | core | rel | rel | — | rel | rel | rel | — | — |
| Linear programming | — | ext | rel | rel | rel | ext | — | — | — | — |
| Coordinate geometry foundations | — | core | core | rel | rel | core | core | core | core | rel |
| Deductive geometry | — | core | core | rel | — | rel | core | core | core | rel |
| Congruence & similarity | — | core | core | rel | — | rel | core | core | core | rel |
| Pythagoras' theorem | — | core | core | rel | rel | core | core | core | core | core |
| Introduction to trigonometry | — | core | core | rel | rel | core | core | core | core | core |
| Mensuration in 3D | — | core | core | rel | — | rel | core | core | core | rel |
| Coordinate geometry of circles | — | core | rel | ext | rel | ext | — | — | rel | rel |
| Advanced trigonometry | — | ext | core | core | core | core | rel | rel | core | core |
| Properties of circles | — | ext | core | rel | — | rel | — | rel | core | rel |
| Loci | — | ext | rel | rel | — | rel | — | — | rel | — |
| Charts & averages | — | core | core | rel | rel | core | core | core | core | rel |
| Measures of dispersion | — | core | core | rel | rel | core | core | rel | core | rel |
| Basic probability | — | core | core | rel | rel | core | core | core | core | rel |
| Permutations, combinations & probability | — | ext | ext | core | rel | core | rel | — | — | rel |
| Normal distribution & z-scores | — | ext | rel | core | rel | core | rel | — | — | rel |
| Statistical literacy | — | core | rel | rel | rel | rel | rel | rel | — | — |
References
Official and secondary sources used when mapping frameworks (verify links periodically).
- HKEAA — HKDSE subject information
- Cambridge International — IGCSE Mathematics (0580)
- Cambridge International — A Level Mathematics (9709)
- College Board — AP Calculus AB
- IBO — Diploma Programme mathematics
- Common Core State Standards — Mathematics
- Singapore MOE — Primary mathematics
- UK Government — National curriculum
- Global curriculum overview (guruforu.com)
Research notes migrated from project curriculum gap analysis (2025–2026). Graph prerequisites follow integer / rational / proportion scaffolding before the live directed-numbers synthesis chapter.